Quotes

"In discussing these [the mechanical and thermal properties of matter], we will find that the "classical" (or older) theory fails almost immediately, because matter is really made up of atomic-sized particles."

Newton's Laws of motion were believe to work on ALL levels for all things, allowing (if you had a large enough computer) for a complete prediction of absolute motion of anything - a baseball, a cloud, a galaxy. But quantum mechanics shows us we are wrong, at least when in comes to the smallest scales of atoms and motions.

Questions:

Key terms:

 Follow along with this chapter using the wonderful Physics 2000 website

For more information on the history of Quantum mechanics, look at Quantum Theory Comes of Age
by Dan Thomas, Department of Chemistry and Biochemistry, University of Guelph,
Canada

For a laymen's introduction, look at Todd Stetl's site at the University of Washington.

Quotes:

"Quantum mechanics is the description of the behavior of matter in all its details, and in particular, of the happenings on an atomic scale.

Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles...."

Light behaves like waves & particles

Electrons behave like particles & waves

Electrons behave like light - so studying electrons can be used as a testbed for studying all kinds of particles & photons.

Questions:

How can we describe things that don't behave in ways that we can understand or predict? Do physicists need to learn poetry and art to help them describe the ineffable?

Key terms:

Schroedinger formulated the "wave equation" for particles, like electrons. The mathematics he used, though, was not deterministic, but rather probabilistic. The equation is really a relationship between the energies a particle may have an the probability function governing the distributions of that energy.

Werner Heisenberg is most famous for the "uncertainty principle", discussed later in this chapter.

Neils Bohr is credited as the first to describe the behavior of electrons in atoms as having specified, quantified, energy levels which can be thought of as complete, integral waves.

Quotes

" So we have to learn about them [things on a small scale] in a sort of abstract or imaginative fashion and not be connection with our direct experience.

We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics."

Questions:

Does the admission of failure for classical physics to explain quantum behavior, of failure to be able to predict anything with absolute certainty, "damage" the public's view of science? Does it benefit science to admit this uncertainty, or to make it even more mysterious, so that it seems ONLY a trained "scientist" can possibly understand the world? Is this different from a religious leader claiming that mortals cannot understand the workings of the universe, or of God(s)?

Key terms:

Quotes

"With this apparatus, we can find out experimentally the answer to the question: "What is the probability that a bullet which passes through the holes in the wall will arrive at the backstop at the distance x from the center?"

Experimental Results with PARTICLES:

- Bullets always arrive in discrete lumps

- The probability distribution for arrival at the backstop is the SUM of the probabilities that the bullets pass through hole 1 and pass through hole 2.

- The bullets pass through EITHER one hole or another, not both. There is NO INTERFERENCE."

Questions:

Why would Feynman use this analogy for quantum mechanics? What does the "bullet" experiment do for us, as 'macroscopically familiar' observers?

Key terms:

Quotes:

"The detector is now a device which measures the intensity of the wave motion. You can imagine a gadget which measures the height of the wave motion, but whose scale is calibrated in proportion to the square of the actual height, so that the reading is proportional to the intensity of the wave.

Experimental results with WAVES:

- Intensity can have any size (no "lumpiness")

- Intensity is spread out (diffracted)

- Intensity obsever when both holes are open is NOT THE SUM of the intensities of either single hole experiment.

- The intensity pattern shows INTERFERENCE."

Key terms:

Intensity = A measurement for waves, in terms of energy per second per unit of length or area. The "intensity" of sunlight is measured in energy received per second for every square meter illuminated (Watts/m^2) The "intensity" of sound waves is measured in energy received per second for every square cm of area struck by the wave (decibels are the common unit, related logarithmically to the same units of Watts/m^2)

Diffraction = The tendency or property of waves (sound, light, even earthquakes!) to "bend" around obstacles or apertures, rather than to travel in sharp, straight paths. Sound waves moving past an open doorway down a hall will "diffract" around the corner, allowing you to hear someone's footsteps. Radio waves moving along a valley floor will "diffract" around hills. Earthquake waves will "diffract" around continental shelves and areas of different density.

Quotes:

"We know the results that would be obtained because there are many experiments that have been done...

If we lower the temperature of the wire in the [electron] gun, the rate of clicking slows down, but still each click sounds the same.

Experimental results with ELECTRONS:

-Arrival of electrons in "lumps", one at a time, identically. (PARTICLE-LIKE)

- The probability distribution at the backstop shows a characteristic inteference pattern. (WAVE-LIKE)"

Questions:

If each "click" represents exactly ONE electron, then shouldn't it be possible to tell exactly whether the click was made from an electron passing through hole 1 or hole 2?

Key terms:

Quotes:

"Proposition A: Each electron either goes through hole 1 or it goes through hole 2.

SUPPORTED by the lumpiness result!

Assuming A [is true], all electrons that arrive ... can be divided into two classes: (1) those that come through hole 1, and (2) those that come through hole 2.

Let us check this idea by experiment.

CONTRADICTED by the interference result!

There is interference

We conclude the following:

The electrons arrive in lumps, like particles, and the probability of arrival of these lumps is distributed like the distribution of intensity of a wave.

Questions:

How does Feynman convey the mystery here? What language and style does he use? Is it effective? Can you imagine him saying this to a class full of eager (?!) physics students? To you?

Key terms:

Quotes:

"Adding a very strong light source, so that the passage of an electron through either hole is "observed" by its effect on the light.

Every time we hear a "click"... we also see a flash of light EITHER near hole 1 or hole 2, but never both at once.

Proposition A is necessarily TRUE

When we watch them, the electrons come through just as we would expect them to come through.... those which we see come through hole 1 are distributed in the same way whether hole 2 is open or closed.

But then, we no longer get the old interference curve, but a new one showing no interference!.

We must conclude that when we look at the electrons the distribution of them on the screen is different than when we do not look."     

Questions:

What does Feynman do with the results of this experiment? Do you see the scientific method here? Relate this process to what he mentions earlier, or to what we read of Galileo and Freud.

Key Terms:

Quotes:

" Is there not some way we can see the electrons without disturbing them?

- try different intensity of light? NO

- try different frequency of light? NO, but...

Then a terrible thing happens. So now, when we make the wavelength longer than the distance between our holes, we see a big fuzzy flash when the light is scattered by the electrons. We can no longer tell which hole the electron when through!

In our experiment we find that it is impossible to arrange the light in such a way that one can tell which hole the electron went through, and at the same time not disturb the pattern.."

Questions:

In what other scientific or social situations does the presence of an observer, or the act of observing a thing or event, CHANGE the event? What do marketing companies do to investigate public reactions or opinions? Anthropologists to investigate other cultures? Is this result reallly so surprising?

Key terms:

 Planck's constant = "h"; it has a value of 6.63 x 10^-27 Joule-seconds. It is the ratio of the energy of a package of light (or particle) to its frequency.

See Physics 2000 Website for more information about quantum mechanics.

 Quotes:

"It turns out that for the bullets the wavelengths were so tiny that the interference patterns became very fine."

The wave nature of macroscopic motions, like a baseball, is simply too hard to detect. Quantum mechanically, your motion through space (even your existence in space) CAN be described by a wave, but with a frequency so high as to be indistinguishable from a smooth curve.

Quotes 

We can only predict the odds! This would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. Yes!

It must be recognized that this is a retrenchment in our earlier ideal of understanding nature.

Questions 

What would Galileo make of Quantum Behavior? Freud? Darwin? Or for that matter, Thoreau? Think of what this result means to science, and what science has stood for in our culture since the "scientific revolution".

Quotes 

"The uncertainty principle can be stated mathematically as an inequality - the uncertainty in momentum of a particle times the uncertainty in position will ALWAYS be greater than a constant, known as Planck's constant.

Imagine measuring the momentum "kick" of an electron scattering off the screen:

Now in order to do this it is necessary to know what the momentum of the screen is, before the electron goes through. But remember, according to the uncertainty principle, we cannot at the same time know the position of the plate with arbitrary accuracy."

 Questions:

Consider all of the experiments presented in this chapter, and ask whether spending tax $$ to verify these is worth the expense, if the result ends up that you CANNOT predict what the exact results will be?

  More reading:

Anderson, Mark. (2001) Quantum Mechanics New Horizons. Wired Magazine.

Applications? Look at Google's Directory!

New Scientist Quantum Site